So far, WoW has held to a pattern: every other expansion, we get a new class. In Wrath of the Lich King, we got the Death Knight. In Mists of Pandaria, we got the Monk, and now in Legion we've gotten the Demon Hunter.
Classes are probably the most tricky feature to add to the game - one's class really fundamentally defines how one plays the game, and every new class means the need to come up with a new perspective on the game - and in fact, as specializations have grown far more divergent than they used to be (all Warlocks used to have to maintain Immolate and Corruption on their targets, for example,) a new class really means new perspectives for each of its specs (which is part of the reason there's only two specs for Demon Hunters.)
There is also the question of class fantasy - something that Legion has sought to really build on.
Most WoW classes fit into classic RPG class archetypes. I'll confess that I'm a newcomer to D&D, having only played 5th Edition, but if you compare the classes offered in the current Player's Handbook, WoW covers most of them (combining a couple) but also contains stuff that isn't really covered. There's nothing quite like a Shaman in D&D, for example, and certainly not Demon Hunter (though given that D&D has mechanics for multiclassing, you could maybe combine classes to get closer to these examples.) Death Knights exist in D&D, not as a class, but as a high-level monster (though there's also an option for "Oathbreaker" Paladins that looks similar to Death Knights.)
WoW covers a lot of territory with their classes, and I think that a little overlap is inevitable - it exists already, and would certainly remain an issue in the future. Consider that Death Coil was originally a Warlock ability, and for a time both Warlocks and Death Knights had different versions of it (to be fair, it originally belonged to Arthas in WCIII as a rather straightforward mirror of Holy Light.) When Demon Hunters were introduced, Demonology Warlocks had to be rebuilt from the ground up because Metamorphosis - an iconic Illidan ability from WCIII - needed to be given to Demon Hunters.
We've got two classes that are "nature" themed (but focusing on different aspects of nature.) We've got two "Holy" classes who borrow a lot of Western religious imagery. We've got an East Asian martial-arts class. We have a class that's all about the undead and disease. We've got a classic wizard archetype. We have two classes that bend demonic magic to their will. We have a class that fits the outdoorsman/wilderness-survival archetype. We have a stealthy assassin.
The only really fresh territory I can think of is someone who uses mechanical devices and technology to fight, but in fact, you could argue that Survival Hunters already kind of do this (and of course, there's the Engineering Profession, which means any class has access to this.)
It's not a totally invalid point of view to think that WoW has enough classes - that we're sufficiently covered. But given the excitement that a new class generates, I think Blizzard will try to do them if they can.
It's very possible that I've missed out on some class fantasy that would totally stand on its own, but I think most future class ideas would have to tread on some familiar territory. So here are some ideas:
Actually summoning the dead has become a far less universal thing for Death Knights, with Unholy being the only spec that is really built around it. Unholy would certainly take a hit if Necromancers were introduced.
Still, the thought of a ranged caster class that raises the dead is by no means unprecedented in RPGs. Necromancers would also present a great opportunity to have a "dark" themed healing spec. Most of WoW's healing specializations have a heavy "good guy" theme, with only Discipline using anything dark (and only in balance with the light.) Shamans are at worst ethically neutral. With a Necromancer you could easily create a whole lot of dark-themed healing spells (something that I bet Death Knights and Forsaken characters would feel a lot more comfortable with.)
In terms of DPS, it wouldn't be too hard to come up with something similar to the Diablo II (and soon III) Necromancer, using conjured shards of bone and that sort of thing against your enemies. The problem is that raising the dead to fight for you risks being very similar to the Demonology Warlock spec (and they just got a huge redesign!) Even if you make your undead minions all temporary, that's still basically what Demonology does with its Imps and Dreadstalkers.
And of course, you'd have to find a flavorful way to distinguish these guys from Death Knights. The Scourge doesn't exactly have a monopoly on Undeath in Azeroth, but it's pretty close. We've already seen the Death Knights rebel against it and break away.
That said, the current Lich King is far less antagonistic to the world than the previous one was, so perhaps Necromancers could be the face of a new, more... well, not friendly, but useful Scourge. On the other hand, you'd basically have to have a second Scourge expansion to introduce Necromancers, and I think that's going to either require Bolvar to go evil or to be deposed, so...
I don't know what game it was that made me think this was a common RPG class, but I've always wanted to combine glowy arcane magic with heavy armor and a big old warhammer.
Mages really have a monopoly on Arcane magic in WoW. Warlocks sort of fit in the same "magical scholar" trope, but you don't see anyone really bringing their brains as their main assets to the front lines (except Holy Paladins who make use of their mastery.)
Unfortunately there's not really much precedence in the lore for this one, and I'm not sure we need another tank/melee DPS hybrid (giving them a ranged spec would really emphasize the question of "why not just be a mage?")
So this one actually has precedence, as WCII had Gnomish Tinkers (back then I think the factions' units were mirrored, with the Horde version being the Goblin Alchemist.) This would be a great opportunity to allow another class to use ranged weapons.
It's also pretty easy to imagine a tech-based class performing just about any role - using energy shields to protect oneself or shooting healing beams at their allies. Again, I think that the game needs more ranged DPS specs (despite the addition of three classes, there's one fewer now than there was originally, depending on how you counted Vanilla Survival.)
Something Old God Themed:
Personally I love that Shadow Priests have had their connection to the Old Gods made a bigger part of the theme. It was always suggested - their main filler has always been Mind Flay, and if you know anything about Mind Flayers from D&D, well, they're very Old God-like (Faceless Ones are basically WoW's version of Mind Flayers.)
Still, that's just one spec, and I know that some players preferred to skew more Gothic than Lovecraftian in their interpretation of the Shadow Priest flavor.
The thing is, I don't really know how to reflect Eldritch Abominations in class form, or even what to call such a class. ("Cultist?") And obviously, you have to find a way to make them good guys without giving up their powers (though if they did it for Death Knights, they can find a way.)
I think anything Lovecrafty in class form would have to involve transformation - "Body Horror" being a staple of the Cosmic Horror genre. The question is then how to make sure that it feels different from Druids' shapeshifting, Demon Hunters' Metamorphosis, and Shadow Priests' Shadowform and Void Form.
Barbarian's tough, because some differentiate it from Warriors while others wouldn't. In D&D, there's a clear distinction between they (boringly-named) Fighter, which is your professional soldier/master of arms and the Barbarian, who has a lot of traditional spiritual powers to supplement their fight style.
If Warriors were just Arms and Protection, it would be simple to make this distinction. But Fury really embodies a lot of the Barbarian aesthetic - the over-the-top wielding of two two-handed weapons and even the fact that you take more damage while you're enraged (in D&D, Barbarians don't wear heavy armor, but have similar defensive bonuses.)
You'd probably have to really heavily play up the spiritual side of the Barbarian if you wanted to fit it into WoW.
Though again we have the "don't we have enough melee/tank hybrids?" problem.
If I were designing WoW in 2004, I would have made Discipline a DPS spec. Today it's a kind of hybrid healer/dps spec, but I would have made it a straight-up DPS spec and had Holy as the one healing spec for Priests. It would even be easy to distinguish Discipline mechanically from Shadow. Shadow is based on stacking up DoTs on targets, while Discipline could have been about direct-damage with offensive Holy spells.
So an Inquisitor class would basically be that. The thing is, it really, really overlaps with Priests, and that's really the only spec I could come up with for the class. A healing Inquisitor would basically be a Holy or Discipline Priest.
We only have one Holy DPS spec, which is Retribution. And while Ret sits very comfortably in a familiar RPG archetype, there's plenty of room, I think, for a Holy caster DPS spec.
But I think the far more likely (and I'm not saying that it is likely - just that it's more likely) scenario is that they'd do to Discipline what they did to Survival - rebuild it to perform a different role. Though in this case it would be a far more serious redesign (more akin, perhaps, to making Blood tanking-only and making Frost and Unholy DPS-only.)